Example: Cards Section
Research Question: When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?
I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 Hearts (♥), 8 Diamonds (♦), 8 Spades (♠), and 11 Clubs (♣).
Minitab® – Conducting a Chi-Square Goodness-of-Fit Test
Summarized Data, Equal Proportions Section
To perform a chi-square goodness-of-fit test in Minitab using summarized data we first need to enter the data into the worksheet. Below you can see that we have one column with the names of each group and one column with the observed counts for each group.
| C1 | C2 | |
|---|---|---|
| Suit | Count | |
| 1 | Hearts | 13 |
| 2 | Diamonds | 8 |
| 3 | Spades | 8 |
| 4 | Clubs | 11 |
- After entering the data, select Stat > Tables > Chi-Square Goodness of Fit Test (One Variable)
- Double-click Count to enter it into the Observed Counts box
- Double-click Suit to enter it into the Category names (optional) box
- Click OK
This should result in the following output:
Chi-Square Goodness-of-Fit Test: Count
Observed and Expected Counts
| Category | Observed | Test Proportion |
Expected | Contribution to Chi-Sq |
|---|---|---|---|---|
| Hearts | 13 | 0.25 | 10 | 0.9 |
| Diamonds | 8 | 0.25 | 10 | 0.4 |
| Spades | 8 | 0.25 | 10 | 0.4 |
| Clubs | 11 | 0.25 | 10 | 0.1 |
Chi-Square Test
| N | DF | Chi-Sq | P-Value |
|---|---|---|---|
| 40 | 3 | 1.8 | 0.615 |
All expected values are at least 5 so we can use the chi-square distribution to approximate the sampling distribution. Our results are \(\chi^2 (3) = 1.8\). \(p = 0.615\). Because our p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to conclude that the proportions are different in the population.
Note! Section
The example above tested equal population proportions. Minitab also has the ability to conduct a chi-square goodness-of-fit test when the hypothesized population proportions are not all equal. To do this, you can choose to test specified proportions or to use proportions based on historical counts.